Clipping Polygons Dr Nicolas Holzschuch University of Cape Town Modified by Longin Jan Latecki Sep. 11, 2002

Map of the lecture Problems in clipping polygons Clipping polygons –against one edge of the window –against the whole window Clipping other shapes Accelerating the clipping

Clipping a polygon Different possible cases We have to fill the result of clipping

A polygon must be filled We have to fill the result: –must indentify the new edges –the result must be closed Window Polygon being clipped Resulting polygon

Several new polygons Clipping a polygon may result in several new polygons: Window Polygon being clipped Resulting polygons The data structure must provide for this

Clipping a polygon: algorithm Start by clipping against a window boundary Do each polygon edge in turn Clip each polygon edge against the boundary: –If leaving, connect to latest entering –If entering, connect to latest leaving

Polygon against boundary Outside

Polygon against boundary Outside Inside

Polygon against boundary

Connect

Polygon against boundary

Polygon against window Do each window boundary in turn For each window boundary, clip the polygon using previous algorithm The result is a closed polygon or several closed polygons These are fed to the next window boundary

Polygon against window First edge

Polygon against window Second edge

Polygon against window Third edge

Polygon against window Fourth edge

Clipping Polygons: conclusion A more complex algorithm Algorithmic complexity: 4 times the number of edges Easy to implement using standard languages

Other shapes (circles) Convert the shape to polygon, then clip the polygon –problem: too many edges on the polygon Clip the shape during rasterization –problem: rasterizing invisible parts –can be accelerated by eliminating parts that are trivially invisible

Accelerating clipping Clipping can be a costly step Optimization: –use extents and don’t clip parts that are: trivially invisible trivially visible

Extents Compute the x-extent and the y-extent of the shape: xminxmax ymax ymin

Trivial accept/reject Check the extent with the window: ACCEPT REJECT

Trivial accept/reject Spend some time doing a trivial test Gain more time by avoiding complex computations A common idea to many computer graphics algorithms